Search for single top production via FCNC at LEP at sqrt(s) = 189-208 GeV

A search for single top production (e+e- ->t cbar) via Flavour Changing Neutral Currents (FCNC) was performed using the data taken by the DELPHI detector at LEP2. The data analysed have been accumulated at centre-of-mass energies ranging from 189 to 208 GeV. Limits at 95% confidence level were obtained on the anomalous coupling parameters kappa_gamma and kappa_Z.

The most prominent signature for direct observation of FCNC processes at LEP is the production of a top quark together with a charm or an up quark in the process e + e − → tc 1 . The strength of the transitions γ → ff ′ and Z → ff ′ can be described in terms of the Lagrangian given in [6]: where e is the electron charge, e q the top quark charge, Θ W is the weak mixing angle and P l (P r ) is the left (right) handed projector. The κ γ and κ Z are the anomalous couplings to the γ and Z bosons, respectively. Λ is the new physics scale. A value of 175 GeV was used for numerical calculations throughout the paper. The relative contributions of the left and right handed currents are determined by the g i and z i constants which obey the constraints: In the approach which gives the most conservative limits on the couplings, the interference term, which depends on g i and z i , gives a negative contribution to the cross-section of the process e + e − → tc. This corresponds to the requirement [6]: The existence of anomalous top couplings to gauge bosons allows the top to decay through t → cγ and t → cZ in addition to the dominant decay mode t → bW . This effect was taken into account in the evaluation of results. Numerical estimates of the expected number of events taking into account the limits on anomalous vertices set by the CDF collaboration [7] can be found in [6]. This paper is devoted to the search for FCNC processes associated to single top production at LEP (e + e − → tc). Limits are set on the anomalous couplings κ γ and κ Z in the most conservative approach. The t quark is expected to decay predominantly into W b, giving distinct signatures for the leptonic and hadronic W decays. For each decay mode a dedicated analysis was developed. In the semileptonic channel two jets and one isolated lepton (from the W leptonic decays, W → lν l ) were searched for. In the hadronic channel four jets were required in the event (two of them from the W hadronic decays, W → qq ′ ). A nearly background-free signature is obtained in the semileptonic channel, but the branching ratio is relatively low. In the hadronic channel, the W decays give an event rate about two times higher, but the background conditions are less favourable.

The DELPHI data and simulated samples
The data collected with the DELPHI detector [8] at √ s = 189 − 208 GeV, well above the tc production threshold, were used in this analysis. The integrated luminosity used for each centre-of-mass energy bin is given in Table 1. The data collected in the year 2000 at energies up to 208 GeV are split into two energy bins 205 GeV and 207 GeV for centre-of-mass energies below and above 206 GeV, respectively. The 189,192,196,200,202,205 and 207 GeV energy bins correspond to average centre-of-mass energies of 188. 6, 191.6, 195.5, 199.5, 201.6, 204.8 and 206.6 GeV, respectively. While for the semileptonic channel the two last energy bins were considered separately, they were considered together in the hadronic channel. The background process e + e − → Z/γ → qq(γ) was generated with PYTHIA 6.125 [9]. For µ + µ − (γ) and τ + τ − (γ), DYMU3 [10] and KORALZ 4.2 [11] were used, respectively, while the BHWIDE generator [12] was used for Bhabha events. Simulation of fourfermion final states was performed using EXCALIBUR [13] and GRC4F [14]. Two-photon interactions giving hadronic final states were generated using TWOGAM [15]. Signal events were generated by a standalone simulation program interfaced with PYTHIA 6.125 [9] for quark hadronization. The generation of the signal events was performed with radiative corrections included. The SM contribution is known to be very small (Br(t → (γ, g, Z)+c(u)) < 10 −10 [2]) and was not taken into account. Both the signal and background events were passed through the detailed simulation of the DELPHI detector and then processed with the same reconstruction and analysis programs as the real data.  Table 1: Luminosity collected by DELPHI and used in this analysis for each centre-of-mass energy (see text for details).

Hadronic channel
In the hadronic channel, the final state corresponding to the single top production is characterized by four jets: a b jet from the top decay, a spectator c jet and two other jets from the W hadronic decay.
In this analysis the reconstructed charged particle tracks were required to fulfil the following criteria 2 : -momentum p > 0.4 GeV/c; -momentum error ∆p/p < 1; -Rφ impact parameter < 4 cm; -z impact parameter < 10 cm.
Tracks seen by only the central tracking devices (Vertex Detector and Inner Detector) were rejected. Neutral clusters were required to have an energy of at least 400 MeV.
Events with the visible energy > 100 GeV and at least 8 charged tracks were selected for further processing.
The information of the DELPHI calorimeters and tracking devices was used to classify charged particles as electrons or muons according to standard DELPHI algorithms [8]. A well-identified lepton was designated as a "standard" lepton. Whenever some ambiguity persisted the lepton was called a "loose" lepton. To each lepton tag there corresponds a given detection efficiency and misidentification probability [8]. Events with leptons with momenta above 20 GeV/c, identified as at least "standard" electrons or "loose" muons, were rejected.
The LUCLUS [9] algorithm with d join = 6.5 GeV/c was then applied to cluster the event into jets. Events with 4, 5, or 6 jets were selected and forced into a 4-jet topology. Each of the three most energetic jets must contain at least one charged particle. The preselection was completed by requiring the event visible energy and combined b-tag parameter [16] to be greater than 130 GeV and −1.5, respectively. The energies and momenta of the jets were then rescaled by applying a constrained fit with NDF = 4 imposing four-momentum conservation [17].
The assignment of jets to quarks is not straightforward as the kinematics of the event varies strongly with the energy. Near the tc production threshold both quarks are produced at rest and the subsequent top decay (t → W b) produces a high momentum b quark. However, at higher LEP centre-of-mass energies the c quark becomes more energetic with momentum values up to 30 GeV/c. Four different methods of jet assignment were considered: 1. the jet with highest b-tag parameter [16] was the b jet candidate and the least energetic jet (among the three remaining jets) was the c jet candidate; 2. the most energetic jet was the b jet candidate and the least energetic one was the c jet candidate; 3. the jet with highest b-tag parameter was the b jet candidate and two jets were assigned to the W according to the probability of the 5-C constrained fit; 4. the most energetic jet was the b jet candidate and two jets were assigned to the W according to the probability of the 5-C constrained fit.
All the above studies were performed and the highest efficiency for the signal and strongest background suppression was obtained with the first method. This method was used in the hadronic analysis for all centre-of-mass energies. Method (2), well suited at the kinematic threshold of single-top production, was less efficient at the highest LEP energies because the energy of the b jet becomes comparable to the energies of the other jets.
After the preselection, signal and background-like probabilities were assigned to each event based on Probability Density Functions (PDF) constructed with the following variables: • the event thrust value [18]; • the event sphericity [18]; • the event b-tag calculated with the combined algorithm [16]; • the energy of the jet assigned as b jet (E b ); • the energy of the most energetic jet in the event (E max ); • the ratio of the energies of the least and most energetic jets (E min /E max ); • the invariant mass of the two jets assigned as originating from the W decay (M W ); • the absolute value of the reconstructed W momentum (P W ).
Examples of these distributions are shown in figures 1 and 2, after the preselection.
All eight PDF were estimated for the signal (P signal i ) and background (P back i ) distributions. They were used to construct the signal L S = 8 i=1 P signal i and background based on the ratio of the likelihoods was then constructed for each event. Figure 3 shows the discriminant variable distribution and the number of accepted events, at √ s = 205 − 207 GeV, as function of signal efficiency for a top mass of 175 GeV/c 2 . Events were selected by applying a cut on the discriminant variable ln(L S /L B ), dependent on the centre-of-mass energy. Its value was chosen to maximize the efficiency for a low background contamination. The number of data events and expected background from the SM processes (mostly W W background) passing the likelihood ratio selection are shown in Table 2

Semileptonic channel
In the semileptonic channel, the final state corresponding to single top production is characterized by two jets (a b jet from the top decay and a spectator c jet) and at least one isolated lepton from the W leptonic decay.
At the preselection level, events with an energy in the detector greater than 20% of the centre-of-mass energy and at least 7 charged particles were selected. The identification of muons relies on the association of charged particles to signals in the muon chambers and in the hadronic calorimeter and was provided by standard DELPHI algorithms [8].
The identification of electrons and photons was performed by combining information from the electromagnetic calorimeter and the tracking system. Radiation and interaction effects were taken into account by an angular clustering procedure around the main shower [19].
Isolated leptons (photons) were defined by constructing double cones centered around the axis of the charged particle track (neutral cluster) with half-opening angles of 5 • and 25 • (5 • and 15 • ), and requiring that the average energy density in the region between the two cones was below 150 MeV/degree (100 MeV/degree), to assure isolation. In the case of neutral deposits, no charged particle with more than 250 MeV/c was allowed inside the inner cone. The energy of the isolated particle was then re-evaluated as the sum of the energies inside the inner cone. For well identified leptons or photons the above requirements were weakened. In this case only the external cone was used and the angle α was varied according to the energy of the lepton (photon) candidate, down to 2 • for P lep ≥ 70 GeV/c (3 • for E γ ≥ 90 GeV), with the allowed energy inside the cone reduced by sinα/sin25 • (sinα/sin15 • ).
Events with only one charged lepton and no isolated photons were selected. No other specific criteria were additionally applied to perform lepton flavour identification.
All other particles were then forced into jets using the Durham jet algorithm [20], which is based on a scaled transverse momentum method. Two-jet events were selected by a cut on the value of the corresponding resolution variable y at the transition between one and two jets: −log 10 (y 2→1 ) ≥ 0.45 . The most energetic particle in each jet had to be charged. It was required that the momenta of the lepton and jets were greater than 10 GeV/c and 5 GeV/c, respectively. Polar angles of the lepton and of the two jets were required to be in the region 20 • ≤ θ lep ≤ 160 • and 10 • ≤ θ j1,j2 ≤ 170 • , respectively. The missing momentum polar angle had to be above 20 • and below 160 • and the combined b-tag parameter [16] of the most energetic jet was required to be greater than −1.1.
The energies and momenta of the jets, the lepton and the momentum of the undetected neutrino (assumed to be the missing momentum) were calculated from four-momentum conservation with a constrained fit (NDF=1). Events with χ 2 lower than 7 were accepted, provided the invariant mass of the neutrino and the isolated lepton was below 125 GeV/c 2 . The most energetic jet was assigned to the b quark and the second jet to the c quark. The top mass was reconstructed as the invariant mass of the b jet, the isolated lepton and the neutrino four-momenta. Figures 4 and 5 show some relevant distributions for data and MC, after the preselection and for √ s = 205−207 GeV. The number of events at preselection and final selection levels are given in Table 3 for each centre-of-mass energy. Most of the background comes from SM e + e − → W W events.
After the preselection, signal and background-like probabilities were assigned to each event (as for the hadronic channel) based on PDF constructed with the following variables: • momentum of the less energetic jet; • more energetic jet b-tag variable [16]; • reconstructed mass of the two jets; • reconstructed top mass; • angle between the two jets; • lepton-neutrino invariant mass; • q l · cos θ l , where q l is the charge and θ l is the polar angle of the lepton; • q j1 · cos θ j1 , where q j1 = −q l and θ j1 is the polar angle of the more energetic jet; • p j1 ·[ √ s−p j1 (1−cos θ j1 j2 )], where p j1 is the momentum of the more energetic jet and θ j1 j2 is the angle between the two jets. This variable is proportional to (m 2 t −m 2 W )/2. i.e., not dependent on the centre-of-mass energy.
The signal (L S ) and background (L B ) likelihoods were used on an event-by-event basis to compute a discriminant variable defined as ln(L S /L B ). A loose cut on the signal likelihood was applied to the events. Figure 6 presents, after this cut, the discriminant variable distribution and the number of events accepted as a function of signal efficiency for √ s=205-207 GeV (assuming a top mass of 175 GeV/c 2 for the signal). There is a general good agreement between the data and the SM predictions. The background distribution has a tail for higher values of the discriminant variable which goes below every data event. Correlations between the variables were studied. Their effect on the likelihood ratio is small. Events were further selected by applying a cut on the discriminant variable ln(L S /L B ), dependent on the centre-of-mass energy. Table 3 shows the number of data and background events which passed the cut for the different centre-of-mass energies. The efficiencies convoluted with the W leptonic branching ratio are also shown. The dominant backgrounds come from SM e + e − → W W and e + e − → qq events.  Table 3: Number of events in the semileptonic analysis at the preselection and final selection levels, for the different centre-of-mass energies. The efficiencies convoluted with the W leptonic branching ratio are also shown for a top mass of 175 GeV/c 2 . Statistical and systematic errors are given (see the systematic errors and limit derivation section).

Systematic errors and limit derivation
Studies of systematic errors were performed and their effect evaluated at the final selection level. The stability of the results with respect to variations on the selection criteria, the PDF definition, the different hadronization schemes and the uncertainty in top quark mass were studied.
Concerning the stability of the results, an independent (and large, compared to the resolution) variation on the selection criteria applied to analysis variables like the missing momentum polar angle, the combined b-tag of the most energetic jet, the W mass, the Durham resolution variable, etc. was allowed. The most significant contributions gave a maximum error of 0.5 events and 0.3% for the expected background and efficiency, respectively. Different smoothing procedures were performed for the PDF definition and their effect is at most 0.5 events (0.4%) for the expected background (signal efficiency). Different hadronization schemes (string and independent) [9] were studied for the signal and their effect contributes at most 0.1% for the signal efficiency error. The uncertainty on the top quark mass is the most important source of systematic errors. It affects not only the total production cross-section but also the kinematics of signal events. In terms of signal efficiency, its effect could be as high as 0.9% for the semileptonic channel (in the mass range between 170 GeV/c 2 and 180 GeV/c 2 ). The effects of such variations (added quadratically) on the final selection criteria are quoted as a systematic error in Tables 2  and 3.
The number of data and expected SM background events for the hadronic and semileptonic channels, the respective signal efficiencies and data luminosity collected at the various centre-of-mass energies were combined to derive limits in the (κ γ , κ Z ) plane using a Bayesian approach [21]. In total, 13 independent channels (6 in the hadronic and 7 in the semileptonic modes) correspond to different √ s values. These channels are fitted simultaneously to extract the limits on the FCNC parameters. The total production cross-section and top FCNC decay widths dependence with κ γ and κ Z were properly considered [6] in the limit derivation.
The effect of systematic errors on the (κ γ , κ Z ) plane limits was considered. Initial State Radiation (ISR) and QCD corrections [22] were also taken into account in the tc total production cross-section. Figure 7 shows the 95% confidence level (C.L.) upper limits in the (κ γ , κ Z ) plane obtained by this analysis. The different filled areas correspond to the allowed regions obtained for different top mass values and Λ = 175 GeV. Due to the s-channel Z dominance, the LEP2 data are less sensitive to the κ γ parameter than to κ Z . The upper limits obtained by the CDF collaboration [7] and ZEUS [23] are also shown in the figure for comparison. The 95% C.L. upper limits on each coupling parameter, setting the other coupling to zero, are summarized in Table 4   Upper limits were also obtained by using only the hadronic and the semileptonic channels separately when radiative corrections to the total production cross-section were taken into account. The values at m t = 175 GeV/c 2 are κ Z (κ γ = 0) = 0.491 (0.547) and κ γ (κ Z = 0) = 0.568 (0.625) for the hadronic (semileptonic) channel alone.

Summary
The data collected by the DELPHI detector at centre-of-mass energies ranging from 189 to 208 GeV were used to perform a search for FCNC tc production, in the hadronic and semileptonic topologies. No deviation with respect to the SM expectations was found. Upper limits on the anomalous couplings κ γ and κ Z were derived. A comparison with CDF [7] and ZEUS [23] is also shown. Results on the search for single-top production were also obtained by the other experiments at LEP [24].   Radiative corrections were taken into account in the total production cross-section at LEP. The CDF and ZEUS allowed regions are also shown for a top quark mass of 175 GeV/c 2 . The ZEUS limits are scaled by a factor of √ 2 because of the difference in the Lagrangian definitions.